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The Higgs Boson was predicted with the same tool as the planet Neptune and the radio wave: with mathematics. Why does our universe seem so mathematical, and what does it mean? In my new book, Our Mathematical Universe, which comes out today, I argue that it means that our universe isn't just described by math, but that it is math in the sense that we're all parts of a giant mathematical object, which in turn is part of a multiverse so huge that it makes the other multiverses debated in recent years seem puny in comparison.

Max Tegmark ponders the mathematical universe

At first glance, our universe doesn't seem very mathematical at all. The groundhog who trims our lawn has properties such as cuteness and fluffiness--not mathematical properties. Yet we know that this groundhog--and everything else in our universe--is ultimately made of elementary particles such as quarks and electrons. And what properties does an electron have? Properties like -1, 1/2 and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we've made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are purely mathematical objects in the sense that they don't have any properties except for mathematical properties. The same goes for the space that these particles are in, which has only mathematical properties--for example 3, the number of dimensions. If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn't sound as crazy anymore.

That our universe is approximately described by mathematics means that some but not all of its properties are mathematical, and is a venerable idea dating back to the ancient Greeks. That it is mathematical means that all of its properties are mathematical, i.e., that it has no properties at all except mathematical ones. If I'm right and this is true, then it's good news for physics, because all properties of our universe can in principle be understood if we're intelligent and creative enough. For example, this challenges the common assumption that we can never understand consciousness. Instead, it optimistically suggests that consciousness can one day be understood as a form of matter, forming the most beautifully complex structure in space and time that our universe has ever known. Such understanding would enlighten our approaches to animals, unresponsive patients and future ultra-intelligent machines, with wide-ranging ethical, legal and technological implications.

As I argue in detail in my book, it also implies that our reality is vastly larger than we thought, containing a diverse collection of universes obeying all mathematically possible laws of physics. An advanced computer program could in principle start generating an atlas of all such mathematically possible universes. The discovery of other solar systems has taught us that 8, the number of planets in ours, doesn't tell us anything fundamental about reality, merely something about which particular solar system we inhabit--the number 8 is essentially part of our cosmic ZIP code. Similarly, this mathematical atlas tells us that if we one day discover the equations of quantum gravity and print them on a T-shirt, we should not hübristically view these equations as the "Theory of Everything," but as information about our location in the mathematical atlas of the ultimate multiverse.

It's easy to feel small and powerless when faced with this vast reality. Indeed, we humans have had this experience before, over and over again discovering that what we thought was everything was merely a small part of a larger structure: our planet, our solar system, our galaxy, our universe and perhaps a hierarchy of parallel universes, nested like Russian dolls. However, I find this empowering as well, because we've repeatedly underestimated not only the size of our cosmos, but also the power of our human mind to understand it. Our cave-dwelling ancestors had just as big brains as we have, and since they didn't spend their evenings watching TV, I'm sure they asked questions like "What's all that stuff up there in the sky?" and "Where does it all come from?". They'd been told beautiful myths and stories, but little did they realize that they had it in them to actually figure out the answers to these questions for themselves. And that the secret lay not in learning to fly into space to examine the celestial objects, but in letting their human minds fly. When our human imagination first got off the ground and started deciphering the mysteries of space, it was done with mental power rather than rocket power.

I find this quest for knowledge so inspiring that I decided to join it and become a physicist, and I've written this book because I want to share these empowering journeys of discovery, especially in this day and age when it's so easy to feel powerless. If you decide to read it, then it will be not only the quest of me and my fellow physicists, but our quest.

--

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark is now available to buy.

(The groundhog image above is courtesy of Max Tegmark and Meia Chita-Tegmark. He's not really called "Max Tegmark" either, but "Mr Hoggles.")

"If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn't sound as crazy anymore."

Unfortunately the mathematics depends on purely physical assumptions. For instance, if the speed of the light pulses (relative to the observer) varies with the speed of the observer, as shown in the following videos, the Einstein-Minkowski mathematics is simply wrong:

Max Tegmark: "Does c depend on observer motion (frame)? No first order effect has been seen. Michelson-Morley experiment hammered it - let's see how..."

Max Tegmark, if you knew that, originally, the Michelson-Morley experiment had shown just the opposite - that the speed of light is variable - your "mathematical universe" would be quite different:

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

"Relativity and Its Roots" By Banesh Hoffmann, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Max Tegmark: "In Section III, we discussed the challenge of deriving our perceived everyday view (the "frog's view") of our world from the formal description (the "bird's view") of the mathematical structure, and argued that although much work remains to be done here, promising first steps include computing the automorphism group and its subgroups, orbits and irreducible actions. We discussed how the importance of physical symmetries and irreducible representations emerges naturally, since any symmetries in the mathematical structure correspond to physical symmetries, and relations are potentially observable. The laws of physics being invariant under a particular symmetry group (as per Einstein's two postulates of special relativity, say) is therefore not an input but rather a logical consequence of the MUH."

I am afraid Einstein's postulate of constancy of the speed of light is absurd and for that reason cannot be a logical consequence of any reasonable "bird's view":

When the observer starts moving towards the light source with speed v, the wavecrests start hitting him more frequently - the frequency he measures shifts from f=c/L to f'=(c+v)/L, where L is the wavelength. Yet special relativity says that, even though the wavecrests hit the observer more frequently, their speed relative to him has somehow remained constant, Divine Einstein, yes we all believe in relativity, relativity, relativity.

In other words, no reasonable "bird's view" will have the following incompatible consequences:

1. frequency shifts from f=c/L to f'=(c+v)/L

2. speed of wavecrests shifts from c not to c'=c+v but to c'=c, Divine Einstein, yes we all believe in relativity, relativity, relativity

Max Tegmark: "Einstein, for example, was the first person to really question the idea that time was just this boring thing that ticks at the same rate for everybody. That led to relativity theory. And I suspect that also today there are a lot of assumptions that we're making about reality which just aren't true."

Unfortunately, the "idea that time was just this boring thing that ticks at...

Max Tegmark: "Einstein, for example, was the first person to really question the idea that time was just this boring thing that ticks at the same rate for everybody. That led to relativity theory. And I suspect that also today there are a lot of assumptions that we're making about reality which just aren't true."

Unfortunately, the "idea that time was just this boring thing that ticks at the same rate for everybody" was true, and by replacing it with the false notion of time ticking differently for differently moving observers (or observers located at different gravitational potentials), Einstein literally killed physics. I think nowadays all theoreticians understand that but many are either afraid to say anything or just restricting themselves to vaguely hinting at the problem from time to time:

Philip Ball: "Einstein's theory of special relativity not only destroyed any notion of absolute time but made time equivalent to a dimension in space: the future is already out there waiting for us; we just can't see it until we get there. This view is a logical and metaphysical dead end, says Smolin."

"...says John Norton, a philosopher based at the University of Pittsburgh, Pennsylvania. Norton is hesitant to express it, but his instinct - and the consensus in physics - seems to be that space and time exist on their own. The trouble with this idea, though, is that it doesn't sit well with relativity, which describes space-time as a malleable fabric whose geometry can be changed by the gravity of stars, planets and matter."

Frank Wilczek: "Einstein's special theory of relativity calls for radical renovation of common-sense ideas about time. Different observers, moving at constant velocity relative to one another, require different notions of time, since their clocks run differently. Yet each such observer can use his "time" to describe what he sees, and every description will give valid results, using the same laws of physics. In short: According to special relativity, there are many quite different but equally valid ways of assigning times to events. Einstein himself understood the importance of breaking free from the idea that there is an objective, universal "now." Yet, paradoxically, today's standard formulation of quantum mechanics makes heavy use of that discredited "now."

The Mathematical Universe idea is correct and can be used to solve Hilbert's sixth problem. The first installment of that is deriving quantum mechanics but more can be proven. For details, see the ongoing series of posts at http://fmoldove.blogspot.com/

You write: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."

Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local").

"But are the laws of nature invariant only to changes in inertial reference frames? How about a trivial invariance: the laws of nature do not change during time evolution?"

However, also because inertial frames are invariant only under the mathematical artifacts of spacetime transformation, whether Galilean or Lorentzian, time does not evolve with the state evolution of invariant inertial frames. This is, in fact, what keeps quantum mechanics from being a mathematically complete theory -- the assumption that t = 1, a trivial constant. The laws of nature are in fact invariant under *space*time evolution.

Florin Moldoveanu: "How is special theory of relativity derived? One starts with the invariance of the laws of nature to changing inertial reference frames. From this you get either the Lorentz transformation or the Galilean transformation, and use the second postulate, that of the constant value of the speed of light, to select between the two choices."

True, even trivially true.

Thomas Howard Ray: "Special relativity is derived from Newtonian mechanics and the Galilean transform, to the limit of the speed of light. One doesn't choose between Galilean and Lorentz transformations -- the domain is continuous. This is important, because it begs the continuity of space with time; i.e., special relativity generalizes to accelerated motion (general relativity) because inertial frames are *not* invariant ("all physics is local")."

Here is a useful link https://myelms.umd.edu/courses/1006355/files/30652429/ deriving the Lorentz transformation in the manner I stated in my post. The link is a lecture note from a 100-level introductory class in mechanics special relativity.

Having no clue on either quantum mechanics or relativity I think it is best to refrain from judging other people's abilities.

"In most textbooks, the Lorentz transformation is derived from the two postulates: the equivalence of all inertial reference frames and the invariance of the speed of light. However, the most general transformation of...

"In most textbooks, the Lorentz transformation is derived from the two postulates: the equivalence of all inertial reference frames and the invariance of the speed of light. However, the most general transformation of space and time coordinates can be derived using only the equivalence of all inertial reference frames and the symmetries of space and time. The general transformation depends on one free parameter with the dimensionality of speed, which can be then identified with the speed of light c. This derivation uses the group property of the Lorentz transformations, which means that a combination of two Lorentz transformations also belongs to the class Lorentz transformations."

The *reason* that special relativity *can* be generalized to accelerated motion (general relativity) is that inertial frames, though equivalent (meaning that every observer's measurements are valid), are not invariant. Einstein explained this exhaustively as the time variance between observers in relative motion.

When you allow that special relativity limits state evolution over purportedly invariant inertial frames by an invariant time operator, you make a rookie mistake worthy only of Pentcho Valev.

General covariance in GR resolves the pathology inherited from SR that limits inertial frames ("the one free parameter"), though only at the price of spacetime singularities. Your thesis cannot get past the singularity problem in continuous function physics; the illusion of completeness is caused by your assumption that space and time are equivalent (vice the real case of spacetime symmetry) which is valid, as your source says, only for rigid transformations of uniform motion. You are too ambitious -- you claim global meaning for local phenomena by an assumption that time is invariant in every frame.

That "all physics is local," though, as Einstein said, depends very much on the continuous functions of differentiable transformations, not your claimed universally rigid transformations of invariant time parameter.

Math is a tool box, not a particular tool. We keep finding the limits of particular tools and then have to invent new ones. It could be many of the assumptions stated here, from space being three dimensional, to multiverses, is more a function of the limits of our current set of tools, than it is about the fundamentals of nature. Those who think the current tools answer everything are like the person with a hammer that thinks everything is a nail.

Why is space three dimensional? Doesn't it grow from the use of a three vector coordinate system to measure space. Measurement only describes features, it does not create the whole. Possibly we could start from the other direction and just assume space is space, an empty void and then accept that dimensions are the tools we find convenient to describe it. We are points of reference and so lines, planes and areas are how we project out from the point that is our view.

How does nature describe space? Looking out on the cosmos; physical spheres, radiant energy and convective processes connecting the two would seem to be nature's most popular 'mathematical' devices. Yet we have this 'blocktime' which reduces the dynamics to static measures of duration. Measurement is not causal, it is only descriptive. Does that mean blocktime is physically real, or does it point to the limits of a particular tool?

Maybe multiverses are simply a consequence of space not fitting into our current tool box.

Thanks John for this interesting comment. Perhaps I'm misunderstanding you: are you arguing that the number 3, the dimensionality of space, is actually not a property of nature but merely some sort of human invention or construct, and might come out to be 2 or 4 or some other number if we developed different mathematical tools (as opposed to simply defining dimensionality differently)?

Particular Cartesian coordinates are definitely to be chosen arbitrarily. Nonetheless, there seems to be no alternative to a description of space in terms of three orthogonal to each other variables. Moreover, I see such description still not entirely in agreement with the obvious fact that there seems to be no preferred point in space to which we could refer anything. The problem does already occur with the 1D line between minus infinity and plus infinity. Mathematicians do not understand the real numbers IR likewise unrelated; they always refer to zero and one. Accordingly, the air can be identified as the reference for acoustic waves. The speed of acoustic waves in air refers to a "block" of air with finite boundaries.

Michelson's 1881/1887 experiment didn't find a corresponding "block" of space. Instead of accepting that there is simply no absolute point of reference for electromagnetic waves in space, FitzGerald, Lorentz, Poincaré, Einstein, Tolman, and many others arrived at the mathematical tool of covariance theory (Michelson spoke of a monster) and spacetime because other alternatives like dragged aether or emission theory proved untenable and leading Wilhelminian mathematicians were self-delighted having created a non-Euclidean geometry as description of the world.

Max, are you aware of Wolfgang Mueckenheim in Augsburg? Mathematicians called him a ultra-finitist because he argues that there is no absolute infinity. I slightly disagree: I am an EE, and to me infinity is a valuable mathematical fiction and also the most appealing option to conceive the universe.

First let me thank you for the reply. We don't get much input from the powers that be here in the gallery.

Yes, 3 dimensions is a very useful descriptive property of space, especially our relationship to it, just as 'blue' and '4 tires' are properties of my pickup truck. The issue is whether it is somehow foundational, or an effective description of particular properties. Rather than attempt to debate the nature of space(typing on a phone), let me argue that it blurs the functionality of said coordinate system for mapping spatial relations. Unless you are going to specify the particular vectors used, space is effectively infinitely dimensional, since multiple systems can be used to define the same space. For example, you could say the Israelis and Palistinians use different coordinates to define the same space.

Then of course there is that timeline used as the fourth dimension. To be continued.

The issue I have with using time as a dimension and putting it in the same category with space is that while we experience time as a sequence of events and thus this impression of the moment of the present moving from past to future, the evident physical process is of a dynamically changing configuration in which those events form and dissolve, thus it is the future becoming past. For...

The issue I have with using time as a dimension and putting it in the same category with space is that while we experience time as a sequence of events and thus this impression of the moment of the present moving from past to future, the evident physical process is of a dynamically changing configuration in which those events form and dissolve, thus it is the future becoming past. For example, it's not that the earth is flowing/existing/whatever, from yesterday to tomorrow, but that tomorrow becomes yesterday because the earth rotates. This makes time an effect of action, rather than the basis for it and there is no blocktime dimension of events, because energy is conserved, so in order to create new information/the future, then old information/much of the past, is erased.

Now all clocks do run at their own rates because they are particular actions. If time really was that passage from past to future we experience, then one would think the faster clocks would somehow move into the future more rapidly, but the opposite is true. They age/burn/process faster and so they recede into the past more rapidly. The tortoise is still plodding along, long after the hare is dead.

Now measures of distance and duration are inter-related, but then so are measures of temperature and volume, but no one talks about the 'fabric of volumetemperature'.

When we measure distance, area, or volume, we are measuring aspects of space, but when we measure time or temperature, we are measuring aspects of motion. Time is to temperature what frequency is to amplitude. Temperature gets dismissed as an average of motion, but since the units in the medium are exchanging energy, they are entropically seeking that average level as a solution. The most elemental state in nature, such as quantum fluctuations, or cosmic background radiation, are more a thermal description, than a temporal one. It's only when you start to pick out individual frequencies that a time function arises.

John's "fabric of volumetemperature" ridicules the fabrication of spacetime.

Let me instead deal with the mathematical relation between an increment of distance and the belonging timespan.

Poincarè was perhaps inspired by d'Alembert when he realized that this relation can be interpreted as a rotation by 90° in a complex plane. In this sense, t times i is orthogonal to x as x is to y and z. In other words, such spacetime doesn't directly belong to reality but to just one arbitrarily chosen out of two complex planes with either positve or negative sign of the imaginary component. Moreover, Poincaré overlooked that a correct transformation into one of the two complex planes requires Heaviside's trick.

Thanks Robert for your comment. I'd be curious to hear whether, after reading my complete argument in the book, you still feel that my point of view is nothing more than a nonsensical play with words, or if you feel that there really is more than one logical possibility for how things can be and that it's interesting to study nature further to find out.

I don't feel that your point is mere word-play. But regardless of "how things can be", I do believe that it is possible to DESCRIBE "how things can be", in multiple ways, all of which are mathematically exact. I can fit a straight line to a set of data points, and I can also fit a Fourier Superposition to them; both may fit the data precisely. But one makes much more intuitive sense (Occam's Razor) than the other.

For this very reason, communications engineers, long ago, abandoned the use of Fourier Superpositions, when attempting to DESCRIBE information carrying signals. It is time that physicists do the same.

Well said. If consciousness isn't occurring within the matter and energy in the brain, could someone please point out where it is taking place or provide some experimental or logical evidence that it is it a new form of matter.

It sounds like we're all in agreement here. In http://arxiv.org/pdf/1401.1219v1.pdf, I used "state of matter" in the same way as we that we refer to solids, liquids and gases as "states of matter" (or "phases of matter"): not new substances made of new types of elementary particles, say, but traditional particles arranged to be able to process information in certain complex ways.

I think that even likening consciousness to a ""state of matter" in the same way as when we refer to solids, liquids and gases", is one giant step too far. However, if one were to say the activity of "traditional particles arranged to be able to process information in certain complex ways", as in neurons and integrated circuits, then one would be a lot closer to the truth.

I think you have missed the point. If you look at the paper Max cited, you will see that he means something quite specific by the phrase "state of matter":

"To classify the traditionally studied states of matter, we need to measure only a small number of physical parameters: viscosity, compressibility, electrical conductivity and (optionally) diffusivity. We call a substance a solid if its viscosity is effectively infinite (producing structural stiffness), and call it a fluid otherwise. We call a fluid a liquid if its compressibility and diffusivity are small and otherwise call it either a gas or a plasma, depending on its electrical conductivity.

What are the corresponding PHYSICAL parameters that can help us identify conscious matter, and what are the key physical features that characterize it?"

I, not Max, capitalized the word physical. My point is that consciousness is not a PHYSICAL process. It is a SYMBOLIC process, based upon a PHYSICAL process. Some physical foundation has to be there, but its "parameters" are largely irrelevant. It is the SYMBOLIC parameters that matter:

It does not matter how I physically construct a symbol like the letter "A". What matters is how I exploit the symbol to symbolize something OTHER than its physical manifestations/parameters.

I don't know how you're reading it, Rob. It appears to me that Max is comparing continuous states of matter (through phase changes) to continuous states of consciousness, as Gell-Mann similarly does in *The Quark and the Jaguar.*

It wouldn't otherwise makes sense to me to speak of consciousness in relation to matter. It would be a metaphysical process, as you seem to be saying.

It is indeed a metaphysical process, in the original sense of the word; that which is beyond physics.

Chemistry is beyond Physics. Biology is beyond Chemistry. Consciousness is beyond Biology. All the "rules" of the lower levels, fail to provide a complete specification of a higher level; the whole is greater than the sum of its parts.

That's just the the thing, Rob. I don't think Max Tegmark takes consciousness as a metaphysical property of nature and neither do I.

Coming from a realist perspective, we can consider such things as, e.g., "the measurement not done" in a quantum experiment as a metaphysically real result. That does not mean, however, that it is independent of the physics.

In the same vein, changing states of matter -- such as those changes in the states of a conscious brain-mind or a finite state machine of any kind -- are continuous with and not independent of the physical laws that facilitate the changes.

""the measurement not done" in a quantum experiment as a metaphysically real result."

Doesn't this blur the distinction between prediction and actualization that is convenient to particular viewpoints, ie. deterministic ones? The experiment not done, no matter how effective the eventual result, is still a prediction. It weakens the principle of falsifiability, which some, apparently Sean Carroll for one, see as inconvenient.

"I don't think Max Tegmark takes consciousness as a metaphysical property of nature and neither do I." But until you do, you will never understand it.

"That does not mean, however, that it is independent of the physics."

Read what I said Tom, not what you wish to hear or think: "It is a SYMBOLIC process, based upon a PHYSICAL process." By what logic do you convert "based upon" into "independent of"?

As I have pointed-out previously, Look-Up Tables are not a "continuous process".

"There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy."

There is more to consciousness than just the simple continuous equations of Physics. The Physics is there. But so is something else; information. As I have pointed-out previously, the equations of Physics are virtually devoid of information. Such equations may say a lot about the flow of mass and energy. But they say almost nothing about the flow of information.

"Such equations may say a lot about the flow of mass and energy. But they say almost nothing about the flow of information."

And can't, because information is discrete. The problem is, to derive information from a continuous function such that the function is not dependent on its information content to define it. If it were so dependent, every bit would be independent of every other bit. This is not, however, how we observe that nature works.

I am not trying to understand consciousness; I am trying, as von Neumann said of mathematical techniques, "get used to it." If consciousness is not identical to computation -- and I don't think it is -- then only the essential foundations of physical matter can explain it.

"every bit would be independent of every other bit." Every bit of INFORMATION *IS* independent of every other - that is the very definition of INFORMATION.

"This is not, however, how we observe that nature works." Exactly! Because all natural processes, other than Consciousness, are sparse-information processes. We do not observe information. We observe data, with a few bits of information scattered within, like needles in a haystack.

"I am not trying to understand consciousness" But Max is. The title of the new paper he cited above is "Consciousness as a State of Matter".

"If consciousness is not identical to computation -- and I don't think it is" Agreed. It is an EFFECT, that is CAUSED by symbolic processing, and is neither identical with nor an effect of numerical computation.

"metaphysical realism is is nothing more than a way of saying that the moon is really there when no one is looking at it."

I think that falls very much in the category of physical realism. Consider what physical cause would require the moon to cease to exist. It would very likely and very quickly affect everyone, whether they were looking or not, So the absence of such an event would compel most logical people to assume the moon currently physically exists. Now it would be a prediction to assume the moon will exist tomorrow. Since the moon only exists in the present, its future existence is probabilistic and thus metaphysical.

Even if you have a theory which says the moons future existence is as real as its current existence, you cannot conduct experiments to prove it, thus the experiment not done can only imply a prediction. Keep in mind that nature conducts innumerable tests of reality on a continuous basis. All of them in and of present conditions.

"Every bit of INFORMATION *IS* independent of every other - that is the very definition of INFORMATION."

It's your definition of information, not mine. As I said, if this were true, we would have no way of deriving discrete information from a continuous function. The world would be totally disconnected, and reality would be identical (as many quantum theorists believe) to the processing of information in a brain-mind or other finite state machine.

"Keep in mind that nature conducts innumerable tests of reality on a continuous basis. All of them in and of present conditions."

Dependence on conditions obviates physical realism. "Physically real," according to Einstein, is that which is " ... independent in its properties, having a physical effect but not itself affected by physical conditions."

". independent in its properties, having a physical effect but not itself affected by physical conditions."

How do you test for something not affected by physical conditions? Like dark matter and dark energy, its sole function seems to be to explain physical conditions whose cause cannot otherwise be determined.

"Every bit of INFORMATION *IS* independent of every other - that is the very definition of INFORMATION."

"As I said, if this were true, we would have no way of deriving discrete information from a continuous function."

Could it be that information is necessarily static, given that dynamics entails change and thus dynamic information would be unstable, to say the least. Meanwhile the larger reality that information is a discrete description of, is inherently dynamic and so collecting information about it, whether a thought, a photograph, or a quantum measurement, means coalescing the desired information out of the dynamic. Thus we have that dynamic continuum and discrete information.

Tom,

"Indirectly."

Yet wouldn't that proof have to remain in the conditional category? Epicycles were pretty effective at predicting eclipses, but that wasn't direct proof of giant cosmic gearwheels. The existence of life is taken as proof of a theological entity, but the lack of direct evidence certainly empowers the skeptics. Presents under the tree is indirect proof of Santa Claus, but....

"Tests for dark matter require no other evidence for existence. It's the nature of dark matter that we don't understand."

Tests for multiverses require no other evidence for existence. It's the nature of multiverses that we don't understand.

Charlie Rose hosted a series of distinguished panelists on recent advances in neurological sciences that included new insights into consciousness arising from brain function. Tegmark's loosely prophesizing a correlation with "states of matter" is not without precedence. The optic nerve bundle has been discovered to concentrate a thousandfold the signals from the retina before the signal in a more consolidated form reaches the brain loci, though there are no structures in the neurons that can be identified with that assimilative process. The series was fascinating and can be found on his website:

"there are no structures in the neurons that can be identified with that assimilative process"

Of course not. Think about it. The information transmission bandwidth of the optic nerve bundle is BILLIONS of times too small to transmit the bandwidth existing in visible light. Consequently, the photo-receptors simply IGNORE all that bandwidth, long before the signal ever reaches the optic nerves. It accomplishes this by AM detecting light's 2.5x1014 Hz bandwidth, using a post-detection bandwidth of only 10 Hz.

in other words:

1) Take the light waveform, W(t)

2) Square each point to form W2(t)

3) Smooth that result (lowpass filter) by a factor of 10,000 billion.

In actuality, these three processes are all accomplished in a single step, by simply absorbing (integrating the "count") the photons. (and must be, because of bandwidth limitations of subsequent processing)

The process you describe may be what happens in the individual rod or cone receptor in the retina, I don't know. What was presented by the researcher was that the electrical pulses from those retinal receptors to the optic nerve, were then condensed before the synaptic connections in the brain. The individual rods and cones of the retina each have specific functions, one might only react to a round shape, another to a diagonal, another to rotation, another to vertical movement, etc. All that specific information transmitted by discrete electrical discharge at the receptor/optic nerve synapse is assimilated into a condensed number of electrical discharges at the nerve/brain synapses, without loss of content. The panelists participating in the series had made clear that analogies with computer circuitry is not relavent to what is being discovered in brain function. Given the credentials of panelists I think cross discipline participation with physicists in a number of areas of research was most likely, and apparent in some matters discussed.

I would recommend the whole series on 'The Brain' presented by Charlie Rose, to anyone with one. jrc

The process I described is, as you observed, happening within individual receptors. In fact, it happens within each individual photo-receptor molecule, since nothing else can deal with all those individual photons.

However, long before any signals are transmitted across the optic nerve, a great deal of signal processing, which DOES involve a "loss of content" is performed on the retina itself. For example, your blurry peripheral vision is generated by combining (sort of like averaging) the outputs of large numbers of individual receptors, into a single channel.

Since the "round shape, another to a diagonal, another to rotation, another to vertical movement" are all occupying more than a single point in the image, the processing obviously must span more than a single point receptor.

"The panelists participating in the series had made clear that analogies with computer circuitry is not relavent to what is being discovered in brain function"

The panelists, to be sure, have great credentials in their field. But their field is not signal processing; their expertise is not relevant to the analysis of the algorithms employed to accomplish the type of effects they are discovering.

"ad hominem". True enough, but there is also such a thing as justifiable ad hominem.

It is a historical fact that the panelists and their colleagues have been unable to "connect the dots" of even the simplest of color visual processes, even though the dots themselves have been around for over a century, and the connection between them was discovered by communications engineers...

"ad hominem". True enough, but there is also such a thing as justifiable ad hominem.

It is a historical fact that the panelists and their colleagues have been unable to "connect the dots" of even the simplest of color visual processes, even though the dots themselves have been around for over a century, and the connection between them was discovered by communications engineers in the mid-1930s.

TO THIS DAY, all these people view the correlation between the frequency of an electromagnetic light-wave and color, to be due to some ad-hoc brain process unlike anything done elsewhere in "computer circuitry".

But it has been known since the 19th century work by Young and Helmholtz, that Color Perception, seems to be based on three "tuned-bandpass-receptors". It has also been known, from Hering's 19th century work, that the tuned-bandpasss-receptor outputs seem to be processed via some sort of Opponent Process. If you examine the web-links I gave, and virtually all other discussions of color perception, you will find no clue as to why these two processes correlate so well with the measurement of frequency. But the answer has been known, to communication engineers, since the 1930s, when Travis patented the double tuned circuit discriminator technique.

I myself have a couple of patents, from over twenty years ago, on a variation of Travis's technique, for which the "opponent process" is not merely highly correlated with frequency, but transduces paired amplitude estimates into EXACT frequency estimates. (see my 2012 FQXI essay for the math details).

My point is that, in spite of the fact that a TRIVIALLY SIMPLE, mathematically exact reason for the correspondence between the Young/Helmholtz/Hering results has been known for decades, the panelists and their colleagues remain TOTALLY ignorant of them.

When someone remains so ignorant of, what in other fields are well-known results, it is difficult to have much confidence in their pronouncements "that analogies with computer circuitry is not relavent to what is being discovered in brain function.".

Since there are dozens of episodes in the Charlie Rose brain series, could you be more specific about the particular episodes that discussed the items mentioned in your first post:

"The individual rods and cones of the retina each have specific functions, one might only react to a round shape, another to a diagonal, another to rotation, another to vertical movement, etc. All that specific information transmitted by discrete electrical discharge at the receptor/optic nerve synapse is assimilated into a condensed number of electrical discharges at the nerve/brain synapses, without loss of content. The panelists participating in the series had made clear that analogies with computer circuitry is not relavent to what is being discovered in brain function."

I would have to troll through those episodes again myself to direct you to the specific one I synopsized, and I dare say that much of what was discussed was in terms that were introductory for the public. Given the highly incorporated nature of research at that level of play these days I would assume that there has been much of what is your own expertise, inclusive of departmental inter-disciplinary participation and correlation. Give me a little time and I'll see if I can weed out what might be of interest to you.

I have no expertise in the field of signals modulation but find it interesting from the standpoint of the observed distinct regions of the full spectrum, interacting with matter so differently. Ground penetration by radar, chromo opacity and transparency, microwave absorption, etc. It's too fertile a field for me to want to get into, though, I'm looking at it more as subject for a good impressionistic painting.

This started with my saying Max Tegmark's premise is not without precedence, and I quite understand your arguments against that possibility. And I do not take that premise to the point of evolving a concept of human consciousness as 'the most beautiful' structure in the universe, maybe that will sell a few more books though. In fact, I can not approach physics without the acute awareness of the very human tether on my comprehension. And I'm personally more comfortable with a generalized idea of math being more like the dimension of unity, the units of which are natural functions no two of which are alike. And as 'Mad Max' points out, the argument is ages old. I like my little background independent workbench. I at least know where it's at.

The episode 'Vision' was originally broadcast on Nov. 24, 2009 and again on Aug. 24, 2010; BUT neither date is listed in The Brain series search page on the Charlie Rose website. I was able to find it listed on www.tv.com/shows/charlie-rose and there it has to be downloaded which I think is a freebie but I have a personal rule not to download from those type of sites so - good luck. It is a little odd that an episode got dropped from CR's own website and there is no query box for notification, but he's a busy guy.

"And what properties does an electron have? Properties like -1, 1/2 and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we've made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are...

"And what properties does an electron have? Properties like -1, 1/2 and 1! We physicists call these properties electric charge, spin and lepton number, but those are just words that we've made up and the fundamental properties that an electron has are just numbers, mathematical properties. All elementary particles, the building blocks of everything around, are purely mathematical objects in the sense that they don't have any properties except for mathematical properties. The same goes for the space that these particles are in, which has only mathematical properties--for example 3, the number of dimensions. If space is mathematical and everything in space is also mathematical, then the idea that everything is mathematical doesn't sound as crazy anymore."

Picking one: The units of Coulombs, for electric charge, are not measurements of words. It is the units that represent the properties, and their physical definitions, in mathematical equations. The numbers count the units. The equations model the patterns observed in changes of velocities of objects. The equations are written using numbers and words, but the patterns being modeled are not those numbers and words. The words are 'words', the numbers are 'words', and the symbols are 'words'. the 'words' are merely signs. The 'words' 'electric charge', for example, are signs that point to where we store meanings so that we may retrieve the meaning of electric charge and thereby remember the physical property whose patterns are being mathematically modeled. However, the words 'electric charge' do not appear in mathematical equations. The word 'coulomb' appears in mathematical equations.

The physical meaning of what 'coulomb' points us to in the mks system of units is: One coulomb is the quantity of charge passing through a section of a conductor in which there is a constant current of one ampere. The ampere is that constant current when present in each of two parallel conductors of infinite length and one meter apart in empty space causes each conductor to experience a force of exactly 2x10-7 newtons per meter. The importance of this definition is to recognize that the ampere is defined in terms of empirical measurements involving force and distance, two of the four fundamental properties in Newton's f=ma. The very empirically founded f=ma models patterns in changes of velocities of objects and not of numbers or words.

"...At first glance, our universe doesn't seem very mathematical at all. The groundhog who trims our lawn has properties such as cuteness and fluffiness--not mathematical properties. Yet we know that this groundhog--and everything else in our universe--is ultimately made of elementary particles such as quarks and electrons."

What the groundhog is telling us is that it consists of objects that have properties that cause effects, some very important ones, that are not all included in the interpretation of the universe provided for us by theoretical physics. A mechanical interpretation of the universe is limited to solving mechanical problems. Mathematics is a tool for modeling a mechanical interpretation of the universe. In other words, mathematics is presently the embodiment of theoretical physics. Theoretical physics includes both mathematical properties, i.e. invented properties, and empirical properties, those which give us our empirical evidence.

"Max Tegmark ponders the mathematical universe" This is a very funny caption.

Hi James - wouldn't you agree that the Coulomb is a somewhat arbitrary unit made up by us humans, and that if we'd discovered that all electric charge is quantized before we defined the Coulomb, we might have instead defined it so that the electric charge was -1 (or +1)?

For the other electron quantum numbers, e.g., spin and lepton number, we've indeed opted for such dimensionless definitions.

I was very happy when you replied to my email few years back. As my theory matured I tried to get your attention to no avail. My guess is that you did not get the chance to see it, OR, the way my theory is presented is unacceptable in the mainstream and hence an...

I was very happy when you replied to my email few years back. As my theory matured I tried to get your attention to no avail. My guess is that you did not get the chance to see it, OR, the way my theory is presented is unacceptable in the mainstream and hence an embarrassment.

I will present it again in case it was the former reason( I am working to fix the second reason). The information that is presented is not complete but the already obtained results should be enough to take notice. I will have more information later.

In This essay I shall derive the laws of nature from a simple mathematical system. The system is derived from the postulate that reality is nothing but a mathematical structure which leads to a simple system that can be simulated to generate many results. The postulate lead to assume particles as made of lines were one end originates in a small region and it extends to all other point in space. The start point and the end point of these lines define space and the length of the line is interpreted as energy, time is just a change of state. So the system unifies space, time matter, energy all in one coherent picture, all emergent from random points and their relations. The simulations generate some basic Quantum Mechanics results and the 1/r law as in quantum field Theory. There are many other results such as the hydrogen 1s level where the universal constants like c, h, e and their relation that lead to Fine Structure constant automatically fall out of the simulation. Two such simulations are carried out; one is Bohr like model and the other Schrodinger like equations solution and show the equivalency. Also, the mass of the electron appear naturally using a simulation which is an extension of the Bohr model. The system automatically displays the non-local behavior and explains the EPR in simple terms and shows the origin of spin(tentative) . Many interesting formulas connecting electron mass, FSC and electron g-factor is produced. While it is shown that coulomb potential is produced by line crossing, Gravity appears(tentative) when lines meet at a region of Planck's length.

Thank you for the reply. I think you were in a hurry and did not push the "view entire post" link which FQXI's way to expand the shortened reply display. There you would have seen the links and the abstract. I repost the links here again to my theory.

" ... if we one day discover the equations of quantum gravity and print them on a T-shirt, we should not hübristically view these equations as the 'Theory of Everything,' but as information about our location in the mathematical atlas of the ultimate multiverse."

Maybe not everything -- yet vastly enough. For if we actually possess a specific location, and given special relativity, we should know for certain that the world is classical at foundation, and that "All physics is local."

Glad to see your book as a sciam book club featured selection. My order is in, and I look forward to a great read.

About our mathematical universe, and about the "diverse collection of universes obeying all mathematically possible laws of physics" (I don't believe this diverse collection exists, Professor Tegmark). Also, the Higgs boson certainly exists but I don't think it gives ANY particle mass (see the part below where I mention DNA). We could say the Higgs FIELD bestows mass if we think of it as a...

About our mathematical universe, and about the "diverse collection of universes obeying all mathematically possible laws of physics" (I don't believe this diverse collection exists, Professor Tegmark). Also, the Higgs boson certainly exists but I don't think it gives ANY particle mass (see the part below where I mention DNA). We could say the Higgs FIELD bestows mass if we think of it as a gravitational field.

“DIGITAL” STRING THEORY AND RENORMALIZATION

Let’s borrow a few ideas from string theory’s ideas of everything being ultimately composed of tiny, one-dimensional strings that vibrate as clockwise, standing, and counterclockwise currents in a four-dimensional looped superstring (“Workings of the Universe” by Time-Life Books – 1991, p.84). We can visualize tiny, one dimensional binary digits of 1 and 0 (base 2 mathematics) forming currents in a two-dimensional program called a Mobius loop – or in 2 Mobius loops, clockwise currents in one loop combining with counterclockwise currents in the other to form a standing current. Combination of the 2 loops’ currents requires connection of the two as a four-dimensional Klein bottle (binary digits fill in the central hole and perfectly adjust the outer edges to fit surrounding subuniverses - simplified, this is like manipulation of an image on a computer screen). This connection can be made with the infinitely-long irrational and transcendental numbers. Such an infinite connection** translates - via bosons being ultimately composed of the binary digits of 1 and 0 depicting pi, e, √2 etc.; and fermions being given mass by bosons interacting in matter particles’ “wave packets” – into an infinite number of Klein bottles.^^ Slight imperfections in the way the Mobius loops fit together determine the precise nature of the binary-digit currents (the producers of space-time, gravitational waves, electromagnetic waves, the nuclear strong force and the nuclear weak force) and thus of exact mass, charge, quantum spin. They would also produce black holes - whose binary digits could, in the case of the sun, come from our star being compressed to 2.95 kms, in which case the pressure increase "shreds" the sun into its binary digits (its mass is relativistically converted into the energy of binary digits). Referring to a Bose-Einstein condensate, the slightest change in the binary-digit flow (Mobius loop orientation) would alter the way gravitation and electromagnetism interact, and the BEC could become a gas (experiments confirm that it does).

** If the material and immaterial universe consists of an infinite connection of transcendentals and irrationals, renormalization might be unnecessary in certain circumstances. This mathematical procedure is regarded as prerequisite for a useful theory and is used in attempts to unite general relativity with quantum mechanics to produce Quantum Gravity and the Theory of Everything. Renormalization seeks to cancel infinities – but in a literally infinite universe, retaining the infinite values might point the way to deeper understanding of the cosmos.

^^ Each one is a “subuniverse” (bubble or pocket universe) composing the physically infinite and eternal space-time of the universe. The infinite numbers make the cosmos physically infinite, the union of space and time makes it eternal, and it's in a static or steady state because it’s already infinite and has no room for expansion. Our own subuniverse has a limited size (and age of 13.8 billion years), is expanding from a big bang, and has warped space-time because it's modelled on the Mobius loop, which can be fashioned by giving a strip of paper a 180-degree twist before joining the ends. (It also has DOUBLE STRANDED, spiralling DNA because the universe is modeled on TWO twisted Mobius loops. Building on a 1919 paper which Einstein submitted to the Prussian Academy of Sciences [“Do Gravitational Fields Play An Essential Part In The Structure Of The Elementary Particles Of Matter?”], DNA - and its particles' mass, as well as its nuclear and electromagnetic forces## - is made of remarkably warped space-time / extremely intense gravity). Referring to the universe’s infinity - Bob Berman’s article "Infinite Universe" (“Astronomy” – Nov. 2012) says, “The evidence keeps flooding in. It now truly appears that the universe is infinite” and “Many separate areas of investigation – like baryon acoustic oscillations (sound waves propagating through the denser early universe), the way type 1a supernovae compare with redshift, the Hubble constant, studies of cosmic large-scale structure, and the flat topology of space – all point the same way.” Support for the article – a) after examining recent measurements by the Wilkinson Microwave Anisotropy Probe, NASA declared "We now know that the universe is flat with only a 0.4% margin of error." - http://map.gsfc.nasa.gov/universe/uni_shape.html;

and b) according to "The Early Universe and the Cosmic Microwave Background: Theory and Observations" by Norma G. Sànchez, Yuri N. Parijskij [published by Springer, 31/12/2003], the shape of the Universe found to best fit observational data is the infinite flat model).

(cntinuing ^^) Discovery.com (March 18, 2010) says: "The universe is not only expanding it's being swept along in the direction of constellations Centaurus and Hydra at a steady clip of one million miles per hour, pulled, perhaps, by the gravity of another universe." (this is called “the dark flow”) Could this be describing evidence of an idea suggested by mathematics’ "Poincare conjecture", which has implications for the universe’s shape and says you cannot transform a doughnut shape into a sphere without ripping it. This can be viewed as subuniverses shaped like Figure-8 Klein Bottles (similar to doughnuts) gaining rips called wormholes when extended into the spherical spacetime that goes on forever (forming one infinite superuniverse). Picture spacetime existing on the surface of this doughnut which has rips in it. These rips loop from, and back to, space-time; providing shortcuts between points in space and time – and belong in a 5th-dimensional hyperspace. A journey along these loops might, at first, appear to take longer – but remember, that trip doesn’t take place in space or time.

## WHY IS GRAVITY WEAK? (C^2 AND THE ATOM)

When Einstein penned E=mc^2, he used c (c^2) to convert between energy units and mass units. The conversion number is 90,000,000,000 (300,000 km/s x 300,000 km/s). Since we'll be dealing with numbers in the trillions of trillions, and since the many particles and atoms require varying amounts of gravity for their formation, a good approximation will be to round up the conversion factor to 10^11. After gravity forms matter, following (succeeding) gravity waves are, we deduce by looking at the example of astronomy's gravitational lensing, concentrated 10^24 times by density (to 10^25). Then they’re further magnified by the matter's density so they achieve EM's (ElectroMagnetism’s) strength (the electric charges and magnetic fields of electromagnetism are 10^36 times gravity's strength) i.e. 10^25 is multiplied by Einstein's conversion factor [10^11] and gives us 10^36. Just as visible light can be absorbed by interstellar dust and re-radiated at infrared wavelengths, the following gravity waves are absorbed by the matter and radiated as longer-wavelength waves (both as electromagnetic waves - possibly gamma rays, or a microwave background – and as gravitational waves which have lost 10^24 of their energy or strength. Though they start with a strength of 10^25 within the atom, they finish with far less energy and a strength that is equal to the gravity waves existing prior to the matter’s formation, which is labelled "1".)

What happens when gravity and electromagnetism interact within an atomic nucleus? If 10^2 gravitons interact with each photon (or 100 photons with each graviton), the strong force is produced (it’s 10^38 times gravity’s strength). There are two ways to produce the weak force (10^25 times as strong as gravity). It could be 1) the normal function of gravity in 10^25 mode when acting over a distance of 10^-18 metres (the weak force’s range) i.e. the weak force IS gravity in 10^25 mode, or 2) the result of EM’s photons interacting with 10^11 anti-gravitons i.e. 10^36 would be divided by Einstein’s speed-of-light conversion and give 10^25. Not only does 2) relate gravity and electromagnetism, but it suggests electromagnetism is converted retrocausally i.e. “backwards” (from 10^36 to 10^25), and also plays a part in mass formation along with gravitation (as Einstein’s 1919 paper stated).

Gluons (the strong force’s carriers) and the W+, W- and Z^0 particles (the weak force’s carriers) have all been discovered – but that doesn’t mean the strong and weak nuclear forces exist independently of gravity and electromagnetism. The nuclear forces might have no existence apart from G (gravitation) + EM (electromagnetism) but could simply be products of graviton-photon interaction: the strong nuclear force could be gravity “added to” electromagnetism (the electromagnetic force combined with 100 gravitons per electromagnetic photon) while the weak nuclear force could be gravity “subtracted from” electromagnetism (the product of the electromagnetic force combined with 100 billion anti-gravitons). Similarly, both G + EM are needed to produce a Higgs boson.

"The essence of mathematics is its freedom". May I ask Max Tegmark to comment on this utterance by Georg Cantor who plays a similar role in mathematics as does Albert Einstein in physics? Both created a lot of paradoxes.

Although I'm a great fan of George Cantor, and fell in love with his hierarchy of infinities as a teenager, it's important to remember that mathematics` doesn't give you complete freedom. For example, if a civilization develops an interest in 3D shapes built out of identical polygons, they'll discover the five Platonic solids: the tetrahedron, cube, octahedron, dodecahedron and icosahedron. They have the freedom to invent whatever names they wan for them, but they don't have the freedom to invent a 6th Platonic solid - it simply doesn't exist!

Fraenkel's 1923 textbook revealed to me that Georg Cantor made a naive mistake when he assumed the entity of "all" of infinitely numbers like something that can be considered as tangible and fix. While I consider aleph_0 (potentially infinite) and aleph_1 (actually infinite, continuous) as reasonable, I wonder if there is any serious justification already for aleph_2. Cantor's naive ideology is not consistent with my logical reasoning. The finitist Hilbert admitted having replaced it by a clever designed set of axioms.

I appreciate you clarifying that in contradiction to Cantor's naivety, "mathematics` doesn't give you complete freedom."

We may hopefully agree on that one has to carefully check what mathematics fits to physical reality.

Some years ago I read partly your publication about 'The mathematical universe'. I assume that your book will explain the subject in a more popular way. That I did not read the whole publication had a reason; I was already familiar with the subject for many, many years. So I agree with your conviction that our universe is totally mathematical. Moreover, your assumption that consciousness can be understand by knowing the mathematical rules that form reality do not shocked me at all. I have the same opinion.

At the other hand, because of your publication I suppose that you are not familiar with the foundational mathematics that rules reality. This is not surprisingly because studying physics is not the easiest way to understand reality, albeit it is impossible to do any research about the subject without some insight in physics.

The main reason that hinder an easy perception of the mathematical reality is the human projection of the sensorial observations within our imagination. We simply have a wrong concept about reality. And when someone - like Parmenides - draw our attention to the discrepancy between our concepts and reality, we refuse to consider the arguments. Because we are - unfortunately - convinced that natural concepts are the right concepts. But we do not realize ourselves that the natural concept is only formed by our physical orientation in space and time.

First, I do not wish to deny your devotion and your right to the "continuous view" rather than the "discrete possibility". I would however hope that you give some consideration to the latter as well, even if just a tiny bit, and see where it could lead. This is in keeping with an eminent mathematician like Penrose's advice, that we should at the least harbour some suspicion that: "If we continue to divide up the physical distance between two points, we would eventually reach scales so small that the very concept of distance, in the ordinary sense could cease to have meaning. It is anticipated that at … 10-35m this would indeed be the case", "We should at least be a little suspicious that (despite the logical elegance, consistency, and mathematical power of the real number system) there might be a difficulty of fundamental principle on the tiniest scales", "This confidence – perhaps misplaced- …", etc. All on p.113, The Emperor's New Mind.

Having tried to cajole you with this preamble, I found this in one of Max Tegmark's published papers (2007), not the book:

"We found it important to define mathematical structures precisely, and concluded that only dimensionless quantities (not ones with units) can be real numbers".

What is your or the possible interpretation of this Tegmark's statement?

Akinbo

(I am posting here rather than the Classical Spheres blog, so as not to distract from Joy's work). I will post my interpretation after yours for comparison.

It's straightforward, Akinbo. As Max Tegmark explains, after noting that the manifold R, metric space R, number field R and vector space R occupy four symmetry groups in a single representation, "Quantities with units may instead correspond to the 1-dimensional vector space over the reals, so that only ratios between quantities are real numbers."

In other words, the universe of relations among dimensionless points is a real structure independent of internal thought processes. Max's philosophy is an extreme realist position, which I share.

My own literal interpretation of "We found it important to define mathematical structures precisely, and concluded that only dimensionless quantities (not ones with units) can be real numbers" is that Length itself being a quantity that is certainly not dimensionless, with the metre as its unit of measure, has a mathematical structure that is not fully in accord with the real number system, even though ratios of length according to Tegmark and yourself can be described by the real number system, (whatever that means).

This is unlike dimensionless quantities such as temperature, colour or ocean salinity to which the real number system is fully applicable on their own without resorting to ratios. Thanks all the same. How about that little suspicion Penrose talked about, is it an unfounded paranoia by the eminent mathematician?

On Nautilus (which John Merryman first brought to our attention) listen to Tegmark's, Why are you suspicious of infinity?

He says he loves the continuum and also finds it very convenient to do physics (like you and Joy), notwithstanding this he still harbours this paranoia for infinity. Must we sacrifice love and convenience for the truth? Just my opinion since Tegmark also says he dislikes philosophers and they make him annoyed by their questions and since I am one I got to be careful...

I agree with Max Tegmark on all those points, including my attitude toward modern and postmodern philosophy (though not philosophers).

Max, Joy and I are rationalists, and science is a rationalist enterprise. As for a rational objectivity sacrificing love (I don't know what you mean by "convenience") for truth -- what makes you think that truth doesn't include love, beauty, morality and ethics in a demonstrably objective way? Spinoza thought that it does; so do I.

Perhaps I'm being naïve, but that seems pretty straightforward to me. I can say that a dimension of 3^10 cm exists, and I can say that 1 sec exists; but when I say 3^10 cm/sec I have a value between both that in and of itself is not of a constant unit, it's a complex of two unitary quantities. It is an element of definition of terms, and it's bare bones English grammar. jrc

"Perhaps I'm being naïve, but that seems pretty straightforward to me. I can say that a dimension of 3^10 cm exists, and I can say that 1 sec exists; but when I say 3^10 cm/sec I have a value between both that in and of itself is not of a constant unit, it's a complex of two unitary quantities."

I find this unclear. Are you saying that cm/sec are not units? Is the expression 3^10 cm/sec = 3^10? I am trying to link up what you say in your paragraph with the above mentioned '...quantities (not ones with units)...'. Numbers count something or they aren't numbers. It seems to me that there is no such thing as a number without units. That 3^10 is 3^10 somethings. Perhaps the point is that the word units pertains to measurements only. Is it that 'things' can accompany a 'real' number while 'seconds' cannot? Is that the distinction that defines a 'real' number? In the case of my holding two apples, is 'apples' a unit? Is my use of '2' representing a 'real' number?

Yes and No, I went to preview and may have prompted the cursor and it partial posted then would accept my rewrite/edit. I'll try to paraphrase.

All our units and numerical place-values are inventions, epi-mathematical if you will. Yet we invent them with the intent to define some real experienced material structure. 3^10 is a number, an abstraction; cm is an...

Yes and No, I went to preview and may have prompted the cursor and it partial posted then would accept my rewrite/edit. I'll try to paraphrase.

All our units and numerical place-values are inventions, epi-mathematical if you will. Yet we invent them with the intent to define some real experienced material structure. 3^10 is a number, an abstraction; cm is an arbitrary unit by which we accept everybody 'knows' in the same way what a line is. But we invent them and apply them over reality; the definition of 'empirical', not a real absolute term in the universal sense. The same applies to 1 sec., but an empirical union of those two non-reals obtains a real value of 3^10 cm/sec applicable to real spacetime, space-time, whatever. It does not establish a universal scale, but a real relational value which does not have a perceptible dimension of it's own to which a 'unit' might be arbitrarily assigned.

You might take a different theoretical approach, but this is how Tegmark defines the terms in a way that is axiomatic, that is how any argument within the context of his theory construct must treat the form of specific definition. The universe appears to have what it needs to bring structure forth, and Tegmark advocates a mathematical structure which manifests itself in our empirical method. The question is not whether one disagrees with the premise, but respecting theoretical discipline at least, whether he has so restricted his definition of terms which he employs, that he has bootstrapped the construct so that it holds itself up, comes full circle, and analytically can be deemed a complete, rather than provisional theory; not to be confused a theory that completely defines it's objective. Discussion of his terminology should be on clarity in 'theory's terms', for it is no argument for the good that supplants another's terms with another definition, and a theory can not be deconstructed by any but it's own.

In my earlier botched post I had cited recent work in infantile development which shows that levels of nueral activity prior to about 12 mos. show a growth of moments of awareness during 'wakeful' periods but not producing a perceptible degree, and that in that stage infants have the inate ability to immediately distinguish between 'one' object and 'two' or 'three', and less frequently 'four'. This might arise in prenatal development of growth and movement of fingers and thumb imprinting digital awareness at a core level of mental processing. Our number system may be an inherited property of genetic mutation evolving our opposable thumb. The universe appears to have what it needs to bring structure forth. Peace - jrc

My argument would be that both the physical process and the math bootstrap themselves upward into ever more complex levels and then fluctuate around the levels of instability. That line of complexity between chaos and order. As I said before, in a void, there is no information.

"The universe appears to have what it needs to bring structure forth" - JRC

What is structure? Bringing structure forth whatever jrc means must imply some smallest irreducible structure? That implies some discreteness to structure.

Bringing structure forth again implies that there was no structure prior to its being brought forth. And if the process is reversible, e.g. like in a Big Crunch, such brought forth structure ends up where it came forth (from no-structure). Following from this, and from Wheeler's 'It from Bit' and 'Bit from It', the universe is doing computations as Lorraine questioned somewhere, because we can represent structure as 1 and no-structure as 0.

Then other matters... On the question of Multiverses, does anybody know what this means? What separates them? If nothing separates them then we still have one universe. If space separates them, then we can traverse the space from one to the other, then there is still one universe. Just like moving from hot temperatures in Africa to freezing temperatures in North America cannot mean multi-earths. Still one earth. Likewise, different 'mathematical climate and physical constants' cannot mean multi-universes. Talking of existing in a different spatial dimension requires physical clarification. Even if you travel through "wormholes" from one universe to another and back, does that justify saying there is not one universe but many universes?

"I thought science as a rationalist enterprise meant that only what could be measured is real?"

No. It means that theoretical predictions correspond to measured results. A phenomenon can be measured, and its meaning remain unknown (e.g., the cosmic background "static" which would be meaningless if not explained by big bang theory).

Or a theory can be well constructed and yet lack correspondence to a measured result. There are many such theories in physics, of course, which is why theorists and experimenters ideally work together to set up experimental protocols to falsify the predicted result.

I would assume it would be to go back and have a top to bottom review of the theory, but the practice seems to be to propose a new force of nature which conveniently fits the gap between theory and observation.

It's a good thing theorists are not the ones building airplanes, because plaster might not be strong enough.

It would seem to be an automatic assumption. I recall Perlmutter et al discovering the discrepancies in redshift and 'Dark Energy' became the immediate assumption. Dark matter seemed to congeal a bit more slowly, as MoND gives it some competition. The flatness issue did not seem to be of huge concern before Guth came up with Inflation. Other issues, such as the Tolman test have simply been ignored.

Given those who did question Big Bang Theory, such as Hoyle, the Burbages and Arp, pretty much got ostracised, it seems even clear evidence of an otherwise infinite universe has to be automatically shoehorned into a finite, expanding model, in order to be in good graces with the community.

I wonder how long before Smolin, Woit, Carroll, or some other big name openly starts to question the cosmological model as well.

Thanks. I take your answer to "On the question of Multiverses, does anybody know what this means? What separates them?" and your answer "The boundary of a boundary is zero" to mean the boundary between our universe and other assumed ones to be zero. To a philosopher, when the boundary between one system and another is zero, they are one system.

Yes,thanks, that was fun. I think we both see that whatever 'math' is, it is what constitutes structure. What else explains the evidence that the electron is the only energy quantity known to uniformly exhibit the same mass and charge, that's not math? jrc

Hi Akinbo: I certainly share your view that we need to question *all* our assumptions about physics, including the rarely questions assumption that truly infinite quantities and truly continuous quantities exist in nature. I talk extensively about this and other "holy" assumptions in the book. Real numbers are so seductively convenient that I use them in all the courses I teach at MIT - but that doesn't prove that they exist in nature! Indeed, many of our biggest problems in physics today, such as the multiverse measure problem, can be traced back to this assumption.

I ran across a comment in Google groups that I think summarizes what you, John, Florin and others have said about a fundamentally discrete reality:

"Tegmark is arguing for finite mathematics, not just finite physics to defeat Godel incompleteness theorem which he sees as fatal to his idea that all reality is mathematics. That's why he moved to a computational universe. But I find it surprising that Tegmark hasn't incorporated quantum computing in his proposal because ultimately reality is quantum. (Bob Zannelli)"

I think the correspondent has realized something that all of you have missed: that were reality fundamentally discrete, quantum computing should be easy.

On the other hands, the continuous functions of a chaotically deterministic universe falsify the illusion of irreducibly discrete entangled elements in superposition.

"Tegmark is arguing for finite mathematics", which I believe must include finite geometry. My essay, if he cares to read it might be of help to his argument but he dislikes philosophers who can help him out of his troubles...

Then, when you say, "something that all of you have missed", does that include Penrose, Fredkin, Wolfram, etc. These are highly qualified mathematical physicists. But I observe your 100% unwillingness to even give these suspicions on discrete physics a consideration. Why not just 99% and give 1% or 0.5% please? I beg of you as a new year resolution :)

Keep in mind that Fredkin and Wolfram are computer theorists, whose research programs depend on the discrete nature of computation and computable functions. Fundamentally, if one were to extrapolate this philosophy (Fredkin calls it digital philosophy) to the foundations of nature, the universe itself should be a computable phenomenon.

Sir Roger Penrose is a different case -- a mathematical Platonist in the tradition of Godel. That is, for Penrose mathematics lives in a world apart from the physical; physical reality could never fit into the mathematical world. Consider the Penrose triangle in this context: one can draw it in two dimensions, or construct it by a set of computer instructions, yet it cannot possibly exist in the three dimensional physical world. I've read Penrose's work on physics and mind; much of it is inaccessible to me, yet of what I do comprehend, I reject the premise that brain-mind and external nature are identical.

Max Tegmark's view conforms to my own of what the world "should be." Though often wrongly confused with Platonism, it is realist in the extreme, such that mathematical structures -- all of them -- are objective external representations of the underlying reality we all share. For this to be true, there must also be a unifying principle in mathematics, identical to the principle that unifies nature.

That's why I think Joy Christian's measurement framework for quantum correlations is a model clue to finding that principle -- a simply connected space of continuous measurement functions. We cannot get such a picture with an assumption of discrete functions that are disconnected or multiply connected. The Christian-Roth computer simulation makes the case for a smooth stable function with discrete random input -- just the way nature appears to work.

"I would make a note that the mathematical point at infinity is actually realized in the compactification of the complex plane, which shifts the discrete and probabilistic measure functions of the complex Hilbert space to the continuous and deterministic functions of a topological model. You might want to look into that to help further strengthen your argument.

"Something else that caught my eye in regard to Newton's idea of spatial translation: ' ... unless we postulate that there are two spaces that everywhere coincide, a moving one and one that is at rest, so that the movement of a part of the moving one involves a translation of that item from the corresponding part of the resting one to a different part of the resting space ... That is crazy (translator's inclusion) ... ' I have to disagree with the translator's editorializing -- Newton's conception is not crazy; it follows directly from his belief in absolute space and absolute time. The duality is necessary -- which Einstein fixed, with Minkowski's model of continuous spacetime, in which neither space nor time are independently real, but rather preserve physical reality in a union of the two."

I hope you see that I am not "suspicious of infinity." I am just suspicious of the idea that there is more than one infinity in the physical world.

Okay. Thanks for the exchange Tom. I was about to hang my gloves, but I just wondered when you said "...a smooth stable function with discrete random input -- just the way nature appears to work". What is the origin of this discrete input? Can a smooth and continuous input provide a discrete output? Can a discrete input give rise to a continuous output? If so how? Or is the continuous nature of the output an illusion? I think to find an answer to these, we must define what 'discrete' means fundamentally. I believe reality and existence has a dual nature, which is probably why the debate has lasted so long. If for example, we start from the premise that what is 'real and exists' is discrete, then between two such 'real and exists', there is 'unreal and not existing' which paradoxically implies 'reality and existence' is smooth and continuous in nature. If on the other hand, we start from the premise that 'reality and exists' is smooth then we cannot have one part of such reality exhibiting a property or undergoing a transition to the exclusion of other parts of same smooth reality, where then is the smoothness? I am not sure but I think this dilemma was mathematically described by Russel's paradox and perhaps illustrated by Godel's proposal. I think the moral is that using only one-side of the coin would not provide a complete picture.

Sure. Consider your foot on the accelerator pedal of your car, or the analog volume control on your stereo.

"Can a discrete input give rise to a continuous output? If so how?"

Here is where Joy Christian's framework is most insightful. The continuous measurement function of correlated elements (quantum correlations) suggests a robustness in the function that subsumes the randomness of discrete events and leaves the function unchanged.

Consider the behavior of soliton waves in this context -- they collide and pass through each other with the same speed and energy amplitude as before the collision. The continuous wave, in other words, behaves as a discrete quantum.

In the Christian framework, the whole wave function -- rather than the solitonic wave which is constrained by a negative feedback condition -- is unconstrained and bounded above and below only by the random discrete quanta that are surprisingly correlated at every scale.

"Or is the continuous nature of the output an illusion?"

Only in the context of how we digitally process information, whether in our brain-minds or by computing machine. It's unfashionable these days to remind ourselves that spacetime in relativity is physically real -- yet a fully relativistic theory must include this continuous function; without it, one ends up with failed theories like Florin's, that try to derive the function from an assumption of a quantized initial condition. It doesn't work.

"--rather than the solitonic wave which is constrained by a negative feedback condition-- is unconstrained and bounded above and below only the random discrete quanta that are surprisingly correlated at every scale."

Topical to this thread and apart from Bell's (theorem that was never a) Theorem; Gimballing the geometric trivector algebras onto a parallelized 3 sphere, allows the geometry to be mapped as a continuum rather then a manifold, and theoretically generating a random point spread that subsumes any number that could be generated discretely. So the upper and lower bounds can be set in projecting scale as a purely operational choice of time parameter for the 3 sphere transitioning the hyperplane. AND that at each scale set, the probability of correlation between discrete and continuous generated points is consistent. Treating this as an abstract of natural functions.

Bell's theorem is true mathematically; i.e., the arithmetic relations are correct. Joy, however, gets the physical result E(a,b) = -a.b for quantum correlations, in a topological framework, which is provably impossible in an arithmetic framework that assumes physical nonlocality and probabilities in linear superposition.

The reason is that non-vanishing topological torsion guarantees a non-probabilistic continuous measurement function. And you're right; it's manifestly local and natural.

If you would take off your "math hat" for a moment, and consider the following, you would have a lot better chance of answering that question:

Biological systems cannot accurately measure or even utilize "phase".

Hence, they cannot employ cleverly crafted phase relationships, as in Fourier Analysis, to either analyze or synthesize ANYTHING. Furthermore, they have no need of such non-causal, infinite basis functions, in order to represent the finite, causal world they inhabit.

The biological senses and their associated processing are almost entirely "Amplitude-Modulation-Only" characterizations of input signals.

Your comment that "human consciousness may have evolved as an accidental by-product of error correction." is closer to the mark. However, it is not random noise, but multi-path and multi-source interference that are the problem. And the solution rests in the use of modulation types that alleviate this problem, rather than sophisticated mathematical coding, to detect and correct errors after they occur.

Ask yourself why the visual system lowpass filters light amplitudes down to a bandwidth of only 10 Hz. When you come upon the correct answer, you will have answered your above question.

I'll give you a hint. While your "physics from scratch" problem may "come without any a priori physical interpretation", the same cannot be said of the "biology from physics" problem.

"The biological senses and their associated processing are almost entirely "Amplitude-Modulation-Only" characterizations of input signals."

E.O. Wilson described the insect brain as a thermostat. Yet it has been shown ants count their steps as a navigation tool. I see the right brain as a thermostat and the left brain as a clock. The non-linear, scalar side to approximate conditions and the linear, sequential side to navigate a path through them.

Counting amounts to amplitude detection. The phase does not matter: you will get the same final amplitude/count regardless of the rate or change-of-rate of the counting. Similarly, a thermostat is sensitive to the amplitude (amount) of heat, but does not need to be referenced to any other event, (which is what phase is all about) in order to determine a temperature value.

"a thermostat is sensitive to the amplitude (amount) of heat, but does not need to be referenced to any other event, (which is what phase is all about) in order to determine a temperature value."

Exactly. Thermostats don't count.

Yes, clocks measure phase, irrespective of the count, but in order to have discrete amplitudes, ie. counting, you need that phasing to separate them.

The point is that insect minds are not just thermostats, they register and record those events. Given they measure distance by footsteps, the phase is spatially regular. While frequency is temporally regular, it is due to crossing distance at a regular rate and arriving at the detector at a constant rate.

Spacing is not required. Ten one-pound bags or one ten-pound bag - it all just adds up to the same thing - ten pounds. If they take 1,000 steps of 1 mm or one step of 1,000, the distance (amplitude) covered is the same. And if they hop, skip and jump the distance in 10 seconds or crawl it over ten hours, it is still the same distance.

Every entity experiences change as a sequence of events, be it an ant, a human, or a cesium atom. Either it is internal activity, or external activity. We think of time as a regular and smooth process, but every action is a consequence of circumstance. There is no universal action and no universal clock, so only a composite of all action would amount to a universal unit of time. Our heartbeat is a form of clock. In fact, mammals are said to have about a billion heart beats, so those with faster rates tend to live shorter lives. Yes, the function of footsteps is to cover distance and it is a stretch to equate distance with duration, which I have also argued against, but both are, in their own way, linear processes, which we measure with scalar units.

So ask yourself, how would an ant count? Does she use numbers she learned in ant kindergarten, or is there a more fundamental rhythm? Walk to the beat? Maybe each step increases amplitude/pressure? Maybe a little mental abacus? Whatever the mechanism, sequence is sequence.

None of that matters. Phase is nothing more than an arbitrary starting coordinate. If I have one ant at coordinate A and another at coordinate B, then the distance between them is |A-B|. If I change the coordinate of each, by an arbitrary phase shift, "p", then all I am doing is creating two new coordinates A+p and B+p. But the distance between them is still just |A-B|.

It does not matter what units they use, or how they measure them or anything else. If the quantity they are measuring is the amplitude (distance), then any phase shift of the coordinate system will yield the same result - the quantity that they are measuring is insensitive to phase shifts.

The question Max asked boils down to: Why don't conscious observes describe the simple distance measurement, as some cleverly constructed, infinite superposition of phase-shifted wave-functions, that all just happen to exactly cancel out, except for the one simple distance term? That is what the "Fourier space" that he refers to is all about.

So ask yourself, how would an ant characterize distance? Does she use numbers she learned in ant kindergarten?

Or does she use Fourier Analysis that she learned in an advanced calculus class at MIT?

"So ask yourself, how would an ant characterize distance? Does she use numbers she learned in ant kindergarten?

Or does she use Fourier Analysis that she learned in an advanced calculus class at MIT?"

Fourier analysis is actually relatively simple, and in fact it is designed to be mathematically simple. The ant's case is much more complicated, because she has nothing more than the initial condition of a branching probability for every time step in which she moves. The ant colony engaging in cooperative tasks, however, leaves a trail of pheromones to guide what would otherwise be a random walk into a channeled path for the *individual ant.* The colony to an external observer, however, finds Fourier analysis useful to integrate the time steps of all the colony members into a holistic pattern that reveals consciously directed activity.

Does that mean that the external analysis is identical to the pervasive consciousness of the colony?

Whether one applies Fourier analysis or any other method to describe the integration of individual apparently random values to a complex system -- to identify that discrete processing of information with the aggregate misses the fundamentally continuous function that the anlysis describes. And therefore misses the meaning of consciousness as a purposeful activity.

So the ant is the individual sequence in the essentially thermodynamic activity of the colony, as it is constantly radiating outward and pulling sustenance inward. Time then is the sequencing of the pattern, be it the individual ant, or the colony as a whole.

You now admit that consciousness is a purposeful activity. Where does this purpose originate? Do you believe that each "fundamentally continuous function" has a purpose? Do you believe that that function knows its purpose? Do you believe that the mere "integration" of any number of such functions will provide them with a purpose?

My point is that it is ultimately unimportant that an analysis and/or description "misses the fundamentally continuous function that the anlysis describes."

Because those functions provide no insight whatsoever into the above "purpose". They are superfluous, as are the "laws" of physics. That does not mean that they are "wrong" or "useless". It simply means that their usefulness does not extend to providing any insight into how a conscious observer behaves.

Fourier Analysis is no different than a screw-driver in this regard. They both have their uses. But explaining why purposeful activity exists is not one of them.

"Where does this purpose originate? Do you believe that each 'fundamentally continuous function' has a purpose? Do you believe that that function knows its purpose? Do you believe that the mere 'integration' of any number of such functions will provide them with a purpose?"

Yes I do. On all counts. What you are not considering is that the integration of these elements may be nonlinear and deterministically chaotic.

"My point is that it is ultimately unimportant that an analysis and/or description 'misses the fundamentally continuous function that the anlysis describes.'"

Unimportant to you personally. So what? No rational system can jettison the correspondence between the objective language of the description and the physical event. I am not ashamed to be a committed rationalist in a rational world.

"Because those functions provide no insight whatsoever into the above 'purpose'. They are superfluous, as are the 'laws' of physics. That does not mean that they are 'wrong' or 'useless'. It simply means that their usefulness does not extend to providing any insight into how a conscious observer behaves."

Then you are a committed anti-rationalist. So we'll never agree.

"Fourier Analysis is no different than a screw-driver in this regard. They both have their uses. But explaining why purposeful activity exists is not one of them."

Demonstrating the correspondence between theory and result, however, is a purposeful activity. It's also the entire business of the rationalist enterprise called science.

So now you have additionally admitted that the "fundamentally continuous function" y=2x has a purpose, and, much more interestingly, that it knows its own purpose.

What is that purpose? How did it communicate that to you? Is there some repeatable, falsifiable experiment by which someone, other than yourself, can induce this function to communicate to them, what it believes its purpose to be, and why it believes that? Does it communicate via ESP?

Rob brought up some interesting issues on "something" and "somewhere" on the Fluctuations, Schmucuations blog and I asked if Rob were a something or a somewhere or both? I now post this as a dialogue hoping it will bring out any new insights...

The State Vs. Tom McEachern

Judge: May Prof. Tom McEachern step into the dock. Please be reminded that you are on oath to...

Rob brought up some interesting issues on "something" and "somewhere" on the Fluctuations, Schmucuations blog and I asked if Rob were a something or a somewhere or both? I now post this as a dialogue hoping it will bring out any new insights...

The State Vs. Tom McEachern

Judge: May Prof. Tom McEachern step into the dock. Please be reminded that you are on oath to speak the truth, the whole truth and nothing but the truth.

Tom McEachern: Yes, your honor.

State Counsel: Please introduce yourself.

Tom McEachern: I am Tom McEachern, a citizen of the FQXi community and professor of theoretical physics with many years experience in continuous and discrete theories.

State Counsel: Are you a "something" or a "somewhere"?

Tom McEachern: I am a "something" and not a "somewhere".

State Counsel: Our witnesses, Mr. Tongue, Ms. Liver and Baby Kidney say you are their residence, do you still say you are not a "somewhere"?

Tom McEachern: Okay, if that is what you mean, I am a place so I am a "somewhere".

State Counsel: Given that you were not here 100 years ago, and you will not be here 100 years from now, will you agree that you are also a "sometime"?

Tom McEachern: Under the circumstances, yes.

State Counsel: So, "something", "somewhere" and "sometime" can refer to the same place at the same time?

Tom McEachern: Yes.

State Counsel: Have you then heard of objections to the marriage of "somewhere" and "sometime" under the family name, space-time?

Tom McEachern: Yes, I have and I take many of the objections as due to misconceptions arising on the macroscopic view.

State Counsel: Can you as a "somewhere" and a "sometime" be separated from each other?

Tom McEachern: That is not possible.

State Counsel: Is the universe, a "somewhere" and a "something"?

Tom McEachern: I believe so.

State Counsel: Is it a "sometime"?

Tom McEachern: Given, my professional experience that there is a beginning to the universe's existence from nothing, which we call a big bang and an end to its existence, which we call the big crunch, I testify to that possibility.

State Counsel: Just as with you, can we separate the universe's properties of "somewhere", "something" and "sometime"?

Tom McEachern: I think it's all one package.

State Counsel: If we continue dividing a length, which is a "somewhere" can we reach a smallest possible "somewhere" or is that smallest geometric object a 'no-where with zero dimension'?

Tom McEachern: (takes a sip of water) A part of me says Yes, there will be a smallest possible "somewhere" and a part says No, such an endeavour will end up no-where.

State Counsel: For the part of you that says No, we seek an adjournment for further questions. For the part that says Yes, is that limit a "something"?

Tom McEachern: It has to be.

State Counsel: Is it a "somewhere"?

Tom McEachern: I think that follows as well since it has the property of locus.

State Counsel: Will that limit also be a "sometime"?

Tom McEachern: (takes a while) If the universe can be a "something", a "somewhere" and a "sometime", I don't see how a part of it will be denied its constitutional rights to enjoy all three privileges. Yes, I don't see why not.

State Counsel: You claim to be an authority in discrete reality…

Tom McEachern: Yes, I do.

State Counsel: What will lie between any two of your length limits? That is between the limit of "somewheres"?

Tom McEachern: There can be no other "somewhere" so it has to be Nowhere.

State Counsel: If that is the case, would you not then say at the limit, the "somewheres" are continuous?

Tom McEachern: A part of me says indeed that would be the case and there can be no talk of discreteness on that basis as the separation cannot be spatially implemented.

State Counsel: Does your other part have a contrary view?

Tom McEachern: Yes, it has.

State Counsel: And what is this?

Tom McEachern: Even though there can be no other "somewhere" or a "something" to separate smallest lengths/space limits into discreteness, remember that the limits are also "sometimes". I suggest this is what does the separation and results in discreteness as the "sometimes" are not equally shared. Time ("sometime") and Space ("somewhere" and "something") would thereby underwrite our existence, our meaning and our function as Wheeler suspected.

State Counsel: Do you have any authority for your claim?

Tom McEachern: Yes, fluctuation on the quantum scale is a modern day description demonstrating the co-existence of "somewhere", "something" and "sometime". Again before this, Leibniz (paragraph 6) had also come to the conclusion that the one and only change Atoms of nature, which to the Pythagoreans is the geometric Point, the unit of extension, the limit of place and divisibility…, the only change available to them is annihilation and emergence from nothing, not being composite things.

State Counsel: No further questions today, your honor.

Judge: Yes, I think I have had enough for today. The court shall adjourn for further cross-examination of Prof. Tom McEachern, if requested.

Your reply gave me some food for thought. You are known like an electron is known, you are named like an electron is named and you are specified like an electron's charge is specified but the truth is only you (and the electron) know where you are. So to me the observer you are somewhere. It is only when I look for you and measure you that I can really say categorically where you are, that is your probability and wave function finally collapses to me the observer. In short to me you are somewhere, something and sometime. To a fundamental particle, it does not care where it is, does not care what it is and does not care what time it is, its time is its time. To it all these are absolute to it and not relative to that of other 'its'.

Now you have seen; "wave function finally collapses to me the observer"

If one must speak of wave-function collapse, then one must realize that one is speaking about the "collapse" of the purposeful activity within the observer's mind, as it contemplates an observed, not a collapse of the observed. The observed simply continues to be whatever, wherever and whenever it is. It is always "in phase" with itself.

Thank you for the reply. I think you were in a hurry and did not push the "view entire post" link which FQXI's way to expand the shortened reply display. There you would have seen the links and the abstract. I repost the links here again to my theory.

The comments mostly deal with whether and to what extent reality is platonically mathematical.

I've been banned for making comments Peter deemed crackpot, so I'l just raise my crackpot ideas here. I wonder how much the problem of reality being seemingly mathematical, but none the less unpredictable, is due to information necessarily being conceptually static and reality/the energy manifesting it, is inherently dynamic. Part of this supposition goes back to complexity theory and how reality is that juxtaposition of order and chaos. Obviously math being the (stable)order defining everything, while the dynamics being the chaotic element constantly upsetting and pushing through the cracks in the system.

I think Peter is on a rampage, attacking everybody in sight. He is accusing people of doing things as if for money and yet he wrote a book that makes money and I don't see anything wrong with that. He accuses people of acting as science spokesman and yet he increasingly doing the same thing to the extreme.

He only allows posts that support his point of view (at least 95%), very strange, never seen that even with Lubosh.

I don't knock Woit for his editing. It's his prerogative. I certainly agree there are problems in physics, but I think it is deeper than those in the field appreciate, because the 'fabric of spacetime' is built into the foundations and it is the grandaddy of projecting mathematical patterns onto the physics. It makes the same conceptual leap of faith as epicycles, assigning agency to the pattern. So Woit is like one of those 80's Russian Communist officials, promoting glasnost and perestroika and thinking it will clear up a few problems and everything will be just fine.

Max Tegmark, author of The Mathematical Universe wrote in 2007, "When considering such examples, we need to distinguish between two different ways of viewing the external physical reality: the outside view or bird perspective of a mathematician studying the mathematical structure and the inside view or frog perspective of an observer living in it.…If the frog sees a particle...

Max Tegmark, author of The Mathematical Universe wrote in 2007, "When considering such examples, we need to distinguish between two different ways of viewing the external physical reality: the outside view or bird perspective of a mathematician studying the mathematical structure and the inside view or frog perspective of an observer living in it.…If the frog sees a particle moving with constant velocity, the bird sees a straight strand of uncooked spaghetti. If the frog sees a pair of orbiting particles, the bird sees two spaghetti strands intertwined like a double helix...". Galileo had also written a profound piece in the past (but not acknowledged by Max) on related ideas on observation from inside/outside the universe, using a ship for analogy.

Now, if the frog performs light experiments, first a Fizeau experiment. It finds that light speed is increased towards it when the current of water is in its direction than when it is against its direction. Again he finds that when the water is stationary and there is no current, equidistant light sources arrive at same time, irrespective of the fact that the earth is moving at 30km/s in orbit around the sun and 380km/s relative to the cosmic microwave radiation depending on choice of reference. Light speed and arrival times from the equidistant sources in different directions is always constant, irrespective of earth motion. The frog then formulates Lorentzian transformation out of ignorance that there is a bird perspective.

How does the bird, see Mr. Frog's experiments? Light from equidistant sources in opposite directions still arrive simultaneously at the frog's position, but in the bird perspective, for the case of the light travelling in the direction of earth motion, it goes c+v, while that in the opposite direction goes c–v. The earth-bound frog itself goes v, the chosen reference earth motion.

Therefore for light travelling in the direction of earth motion, going c+v towards the frog going same direction, that is at –v, its resultant velocity is c+v-v = c. For light travelling in the opposite direction to earth motion, going c–v, towards the frog going opposite direction, that is at +v, the resultant speed is c–v+v = c. Therefore optical phenomena in the water cannot be used to determine the earth's motion as Einstein rightly said. But from the bird perspective, it knows that this is just Galilean relativity for the case when the observer is below deck.

We know the bird. We know the frog. We know light. But we are not sure what the water is or whether there is water at all.

My personal bias for earth-bound dark matter can be found here and awaiting disproof. But more respectable references can be found [1], [2], [3], [4],[5]

In summary, what will be the bird perspective of the null perspective of Mr Frog's Michelson-Morley experiment? Can optical phenomena be the same to both frog and bird, after all visions of spaghetti are conveyed by light?

"The theory of inflation has been spectacularly successful, and is a leading contender for a Nobel Prize. It explained how a subatomic speck of matter transformed into a massive Big Bang, creating a huge, flat and uniform universe with tiny density fluctuations that eventually grew into today's galaxies and cosmic large scale structure, all in beautiful agreement with precision measurements from experiments such as the Planck satellite. But by generically predicting that space isn't just big, but truly infinite, inflation has also brought about the so-called measure problem, which I view as the greatest crisis facing modern physics. Physics is all about predicting the future from the past, but inflation seems to sabotage this: when we try to predict the probability that something particular will happen, inflation always gives the same useless answer: infinity divided by infinity. The problem is that whatever experiment you make, inflation predicts that there will be infinitely many copies of you far away in our infinite space, obtaining each physically possible outcome, and despite years of tooth-grinding in the cosmology community, no consensus has emerged on how to extract sensible answers from these infinities. So strictly speaking, we physicists are no longer able to predict anything at all!"

I think the answer to your implied question of why physicists are unable to predict anything is in the assumption that "physics is about predicting the future from the past." Is it? -- as you say, what past initial condition tells us anything more than that the universe has a past initial condition?

The assumption that the evolution of the universe is based on a sum of probable events, determined by an infinity of probable initial conditions, in fact makes the multiverse certain. To realize this certainty, though, requires abandoning probabilistic measure theory itself -- because that is the *only* option fully consistent with this statement attributed to you: "I really believe that there is this universe out there that can exist independently of me that would continue to exist even if there were no humans."

If existence is continuous though finite -- a finite set of infinite things -- then the world is finite in space and unbounded in time, and probability measure is the scientific idea ready for retirement.

Max Tegmark:"For example, this challenges the common assumption that we can never understand consciousness. Instead, it optimistically suggests that consciousness can one day be understood as a form of matter, forming the most beautifully complex structure in space and time that our universe has ever known. "

I have my own reasons for believing what Max is saying. While consciousness in itself may question the proponent states given as matter distinctions, as consciousness may use it, it still to me questions the state of the most rarefied in order to say what exactly consciousness is at that point.

In a way there is this esoteric feeling of what is transmitted, has a logical and consistent manner, that is somehow lost in it's translation. As a concept/idea of something that is very simple and beautiful, asking for, a description of the reality we live in? So, there is always this attempt to see nature as a partial view of reality, layered, as this expression of consciousness in action, settled to some state of as that defined matter.

In that rarefied form, it is an intellectual struggle to define something that is within, and emotively cast as a fluid state of expression being formed as the person who is restraint to the the final form of there choosing. Memory induced toward repeatability in remembrance of time.

Plato's mathematical foundation is an example of the foundations with which reality is being chosen to be describe as. All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework?

This then goes toward the subject of foundation, now defined as a matter state descriptor as an attempt to understand reality. It's process seeks to be a foundational one. What then ensues as a emergent product from the beginning so as to surmise, that the universe is the way it is, or, that it has a foundational description, of it's possibility. This as a functional expression of the vacua?

Anthropologically this forces one back to question of the relevance of such a stated view, with reality, as to where it is to begin?

Plato Hagel's comment on Plato's mathematical foundation is hard to read for someone whose native language isn't English. Maybe, it is elegant to use only an unexpected question mark after a describing rather than asking sentence.

Isn't the verb missing in the sentence "All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework?"?

"All attempts to describe reality, as a complex view regarded as a simplistic expression, as the choosing of the mathematical framework??"

Physics is about a mathematical approach? Then, from the list of mathematical approaches, which one? The mathematics chosen can only be part of a larger context reality while only revealing "a partial view." It can never be a complete "theory of everything?"

To me, it is a selection based on the idea that, that particular selection, will have a direct affect on what you are doing in physics in terms of it's description of reality.

The inductive, toward simple and beautiful.....as a equation? The complex, to the simple. What "genus figure" resides in the valley.

Also to point toward the understanding of that rarefied state of matter that Tegmark is referring too. The trend toward vacua should have been a clue? Also, that with regard to the Anthropic principle how would such a math be chosen?

I wonder if Plato is your first name, and although Hagel is the German word for hail, this does not explain your grammar to me. Why do you write "Physics is about a mathematical approach?" instead of "Is physics about a mathematical approach?"?

In all, I admit having sometimes problems to understand you. I understand Platonism as claiming that mathematical structures are found rather than invented.

While I don't at all like the anthropic principle, I suspect that there might be flaws in the very basics of mathematics. See my essays. Your question which one is certainly justified.

Why do you write "Physics is about a mathematical approach?" instead of "Is physics about a mathematical approach?"?

In the sense I know that mathematics as a question related to physics is a affirmative. For those recognize this, the answer is obvious as it was to you. To others who would not understand that question, it may be posted as a second option.

The foundational recognition is important. People have debated the struggle with what counts as reality, and to be faced with the question of foundations it is to understand that this push toward describing reality. Albeit a theoretical one, it is based on the information that such a theory is constructed from.

Having read ‘Our Mathematical Universe’ I was both encouraged and surprised that someone in mainstream physics would offer the viewpoint that reality is, in essence, mathematical. To me that equates to reality being solely about relationships, any notion of material absoluteness (whatever is meant by that) becoming irrelevant.

First, would you agree on this assumption?

This is important because to explain consciousness as a natural aspect of the real world, a preliminary step, in my opinion, is to treat the real world purely in terms of relationships. Then the work of Giulio Tononi et al, on qualia existing as the consequence of loops of connectivity in the brain, makes sense. That is, it becomes possible to see the argument for these (neural) loops as having a measure of existence in their own right, and particularly, existence from their own point of view.

All the while the notion of material absoluteness carries any weight, objects (such as neural loops) remain absolved of any additional existential quality (qualia); qualia may exist, but it’s not seen as essential. In this way, the notion of material absoluteness stands in the way of a clear understanding of the subjective experience (see On the Nature of Being). By relegating the notion of material absoluteness to an irrelevancy, those additional patterns (purely due to activity), that one can visualise in addition to the pre-existing relationships describing the physical brain, become more than just interesting behaviour. Instead, they become an unavoidable existential consequence of brain activity that carries equal weight to those permanent relationships defining the physical brain at rest.

Finally then, would you agree that the notion of material absoluteness, that remains prominent in the public eye, stands as the primary barrier to a generally acceptable understanding of the conscious experience?